Nonlinear *-Lie derivations of standard operator algebras

作者：Wu Jing · 发表于：Quaestiones Mathematicae · 年份：2016 · DOI：10.2989/16073606.2016.1247119 · 被引用次数：43 · 研究领域：Advanced Topics in Algebra、Algebraic structures and combinatorial models、Matrix Theory and Algorithms

Let ℋ be an infinite dimensional complex Hilbert space and 𝒜 be a standard operator algebra on ℋ which is closed under the adjoint operation. We prove that every nonlinear *-Lie derivation δ of 𝒜 is automatically linear. Moreover, δ is an inner *-derivation.